Possible medical problems that relate to changes in urinary behaviors include a urinary tract infection or inflammation, blockage or partial blockage, kidney problems, or in the case of excessive thirst and urination, metabolic diseases such as diabetes. It is important to be familiar with the possible signs of a urinary tract infection.
Cats may urinate in unlikely places when stressed, such as a move, new member of the family (human or animal), construction or remodeling in the house, and so on.
Your veterinarian will examine your cat, discuss the behaviors at home, and do the appropriate tests, including an analysis of the urine. The urinalysis will check the concentration of the urine (make sure the kidneys are functioning), and look for red blood cells, inflammatory white blood cells, and crystals. Your veterinarian may also recommend additional blood work or radiographs.
If your veterinarian feels that an infection or blockage is present, prompt medical treatment is necessary. In the event of a blockage or partial urinary blockage, minutes and hours count! Urinary blockage can be fatal.
One thing important to note: cats that have had a urinary medical problem may continue to avoid their litter box even after the medical problem is resolved because they may associate pain or discomfort with the litter box. Or they may deem the box "too dirty" to use if they used it frequently. By doing a deep cleaning (or getting a new litter box) and "reacquainting" your cat with using the litter box, these aberrant behaviors can be corrected.
Reacquainting your cat and modifying the litter box avoidance behavior requires patience, but a good start is a clean litter box and isolating the cat in a small space, such as a bathroom with the litter box available. It is important to remove rugs and other materials that may be more tempting than the litter box.
Care should be given to litter choice as well -- sticking with a non-perfumed litter that your cat is used to is a good start.
In summary, please consult with your veterinarian any time you see your cat urinating outside of the litter box, urinating more (or less) frequently, or straining to urinate. Time is of the essence -- calling sooner is much better than later. By paying attention to litter box habits and acting quickly if there is a problem, you just may save your cat's life.